Engine torque estimation and control systems and methods

ABSTRACT

An engine control system includes: a normalization module configured to normalize, to within a predetermined range of values, a spark timing of an engine and at least one other parameter of the engine, thereby producing a normalized spark timing and at least one normalized other parameter, respectively; a processing module configured to generate a sigmoidal spark timing by applying, to the normalized spark timing, one of (a) a sigmoidal function and a sinusoidal function; and an estimation module configured to estimate a torque output of the engine based on the normalized spark timing and the at least one normalized other parameter using a mathematical model.

INTRODUCTION

The information provided in this section is for the purpose of generallypresenting the context of the disclosure. Work of the presently namedinventors, to the extent it is described in this section, as well asaspects of the description that may not otherwise qualify as prior artat the time of filing, are neither expressly nor impliedly admitted asprior art against the present disclosure.

The present disclosure relates to internal combustion engines and moreparticularly to engine control systems and methods for vehicles.

Internal combustion engines combust an air and fuel mixture withincylinders to drive pistons, which produces drive torque. Air flow intothe engine is regulated via a throttle. More specifically, the throttleadjusts throttle area, which increases or decreases air flow into theengine. As the throttle area increases, the air flow into the engineincreases. A fuel control system adjusts the rate that fuel is injectedto provide a desired air/fuel mixture to the cylinders and/or to achievea desired torque output. Increasing the amount of air and fuel providedto the cylinders increases the torque output of the engine.

In spark-ignition engines, spark initiates combustion of an air/fuelmixture provided to the cylinders. In compression-ignition engines,compression in the cylinders combusts the air/fuel mixture provided tothe cylinders. Spark timing and air flow may be the primary mechanismsfor adjusting the torque output of spark-ignition engines, while fuelflow may be the primary mechanism for adjusting the torque output ofcompression-ignition engines.

SUMMARY

In a feature, an engine control system includes: a normalization moduleconfigured to normalize, to within a predetermined range of values, aspark timing of an engine and at least one other parameter of theengine, thereby producing a normalized spark timing and at least onenormalized other parameter, respectively; a processing module configuredto generate a sigmoidal spark timing by applying, to the normalizedspark timing, one of (a) a sigmoidal function and a sinusoidal function;and an estimation module configured to estimate a torque output of theengine based on the normalized spark timing and the at least onenormalized other parameter using a mathematical model.

In further features, an actuator module is configured to adjust anengine actuator based on the estimated torque output of the engine.

In further features, the at least one other parameter of the engineincludes an engine speed.

In further features, the at least one other parameter of the engineincludes a mass of air per cylinder (APC) of the engine.

In further features, the at least one other parameter of the engineincludes an intake cam phaser angle.

In further features, the at least one other parameter of the engineincludes an exhaust cam phaser angle.

In further features, the at least one other parameter of the engineincludes an equivalence ratio (EQR) of the engine.

In further features, the at least one other parameter of the engineincludes a maximum braking torque (MBT) spark timing of the engine.

In further features, the at least one other parameter of the engineincludes: an engine speed; a mass of air per cylinder (APC) of theengine; an intake cam phaser angle; an exhaust cam phaser angle; anequivalence ratio (EQR) of the engine; and a maximum braking torque(MBT) spark timing of the engine.

In further features, the sigmoid function includes a logistic function.

In further features, the at least one other parameter of the engineincludes a timing of a start of fuel injection of the engine.

In further features, the at least one other parameter of the engineincludes a timing of an end of fuel injection of the engine.

In further features, the processing module is further configured togenerate an exponential engine speed by applying an exponential functionto an engine speed, and the estimation module configured to estimate thetorque output of the engine further based on the exponential enginespeed using the mathematical model.

In further features, the processing module is further configured togenerate an exponential of negative engine speed by applying anexponential function to a negative engine speed, and the estimationmodule configured to estimate the torque output of the engine furtherbased on the exponential of negative engine speed using the mathematicalmodel.

In further features, the processing module is further configured togenerate an exponential maximum braking torque (MBT) spark timing byapplying an exponential function to an MBT spark timing of the engine,and the estimation module configured to estimate the torque output ofthe engine further based on the exponential MBT spark timing using themathematical model.

In further features, the processing module is further configured togenerate an exponential of negative maximum braking torque (MBT) sparktiming by applying an exponential function to a negative MBT sparktiming of the engine, and the estimation module configured to estimatethe torque output of the engine further based on the exponential ofnegative MBT spark timing using the mathematical model.

In a feature, an engine control system includes: a normalization moduleconfigured to normalize, to within a predetermined range of values, amaximum braking torque (MBT) spark timing of an engine and at least oneother parameter of the engine, thereby producing a normalized MBT sparktiming and at least one normalized other parameter, respectively; and anestimation module configured to estimate a torque output of the enginebased on the normalized MBT spark timing and the at least one normalizedother parameter using a mathematical model.

In further features, a processing module is configured to generate anexponential MBT spark timing by applying an exponential function to theMBT spark timing of the engine, and the estimation module configured toestimate the torque output of the engine further based on theexponential MBT spark timing using the mathematical model.

In further features, a processing module is configured to: generate anexponential MBT spark timing by applying an exponential function to theMBT spark timing of the engine; and generate an exponential of negativeMBT spark timing by applying an exponential function to the negative MBTspark timing of the engine, where the estimation module configured toestimate the torque output of the engine further based on theexponential MBT spark timing and the exponential of negative MBT sparktiming using the mathematical model.

In further features, an MBT module is configured to generate the MBTspark timing based on an air per cylinder, an inverse APC, an enginespeed, an intake cam phaser angle, an exhaust cam phaser angle, anequivalence ratio, and an opening of an EGR valve.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description, the claims and the drawings. Thedetailed description and specific examples are intended for purposes ofillustration only and are not intended to limit the scope of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of an example engine system;

FIG. 2 is a functional block diagram of an example engine controlsystem;

FIG. 3 is a functional block diagram of a torque estimation module; and

FIG. 4 is a flowchart depicting an example method of estimating torqueoutput of the engine and controlling engine actuators.

In the drawings, reference numbers may be reused to identify similarand/or identical elements.

DETAILED DESCRIPTION

Internal combustion engines combust an air and fuel mixture withincylinders to generate torque. Under some circumstances, an enginecontrol module (ECM) may deactivate one or more cylinders of the engine.The ECM may deactivate one or more cylinders, for example, to decreasefuel consumption when the engine can achieve a torque request using lessthan all of the cylinders of the engine. The ECM may activate one ormore deactivated cylinders, for example, when the torque requestincreases.

According to the present application, the ECM estimates a torque outputof the engine (e.g., a brake torque) using an engine torque model. Aninput to the engine torque model may include, for example, a sigmoidspark generated by applying a sigmoid (e.g., logistic) function or asinusoidal transformation to a normalized spark timing. Additionally oralternatively, a maximum braking torque (MBT) spark timing may bedetermined and input to the engine torque model to estimate the torqueoutput of the engine. Pre-processing of the inputs to the engine torquemodel improves correlation between model inputs and the estimatedtorque. The engine torque model can also be inverted to estimate aparameter based on a torque of the engine (e.g., a torque request) andthe other inputs to the engine torque model.

Referring now to FIG. 1, a functional block diagram of an example enginesystem 100 is presented. The engine system 100 includes an engine 102that combusts an air/fuel mixture to produce drive torque for a vehiclebased on driver input from a driver input module 104. Air is drawn intoan intake manifold 110 through a throttle valve 112. For example only,the throttle valve 112 may include a butterfly valve having a rotatableblade. An engine control module (ECM) 114 controls a throttle actuatormodule 116, which regulates opening of the throttle valve 112 to controlthe amount of air drawn into the intake manifold 110.

Air from the intake manifold 110 is drawn into cylinders of the engine102. While the engine 102 may include multiple cylinders, forillustration purposes a single representative cylinder 118 is shown. Forexample only, the engine 102 may include 2, 3, 4, 5, 6, 8, 10, and/or 12cylinders. The ECM 114 may instruct a cylinder actuator module 120 toselectively deactivate some of the cylinders, which may improve fueleconomy under certain engine operating conditions.

The engine 102 may operate using a four-stroke cycle or another suitablecombustion cycle. The four strokes of a four-stroke cycle, describedbelow, may be referred to as the intake stroke, the compression stroke,the combustion stroke, and the exhaust stroke. During each revolution ofa crankshaft (not shown), two of the four strokes occur within thecylinder 118. Therefore, two crankshaft revolutions are necessary forthe cylinder 118 to experience all four of the strokes.

During the intake stroke, air from the intake manifold 110 is drawn intothe cylinder 118 through an intake valve 122. The ECM 114 controls afuel actuator module 124, which regulates fuel injection to achieve atarget air/fuel ratio. Fuel may be injected into the intake manifold 110at a central location or at multiple locations, such as near the intakevalve 122 of each of the cylinders. In various implementations (notshown), fuel may be injected directly into the cylinders or into mixingchambers associated with the cylinders. The fuel actuator module 124 mayhalt injection of fuel to cylinders that are deactivated.

The injected fuel mixes with air and creates an air/fuel mixture in thecylinder 118. During the compression stroke, a piston (not shown) withinthe cylinder 118 compresses the air/fuel mixture. While not shown, theengine 102 may be a compression-ignition engine, in which casecompression within the cylinder 118 ignites the air/fuel mixture.Alternatively, as shown, the engine 102 may be a spark-ignition engine,in which case a spark actuator module 126 energizes a spark plug 128 inthe cylinder 118 based on a signal from the ECM 114, which ignites theair/fuel mixture. The timing of the spark may be specified relative tothe time when the piston is at its topmost position, referred to as topdead center (TDC).

The spark actuator module 126 may be controlled by a timing signalspecifying how far before or after TDC to generate the spark. Becausepiston position is directly related to crankshaft rotation, operation ofthe spark actuator module 126 may be synchronized with crankshaft angle.The spark actuator module 126 may halt provision of spark to deactivatedcylinders. Generating spark may be referred to as a firing event. Thespark actuator module 126 may have the ability to vary the timing of thespark for each firing event. The spark actuator module 126 may vary thespark timing for a next firing event when the spark timing is changedbetween a last firing event and the next firing event.

During the combustion stroke, the combustion of the air/fuel mixturedrives the piston away from TDC, thereby driving the crankshaft. Thecombustion stroke may be defined as the time between the piston reachingTDC and the time at which the piston reaches bottom dead center (BDC).During the exhaust stroke, the piston begins moving away from BDC andexpels the byproducts of combustion through an exhaust valve 130. Thebyproducts of combustion are exhausted from the vehicle via an exhaustsystem 134.

The intake valve 122 may be controlled by an intake camshaft 140, whilethe exhaust valve 130 may be controlled by an exhaust camshaft 142. Invarious implementations, multiple intake camshafts (including the intakecamshaft 140) may control multiple intake valves (including the intakevalve 122) for the cylinder 118 and/or may control the intake valves(including the intake valve 122) of multiple banks of cylinders(including the cylinder 118). Similarly, multiple exhaust camshafts(including the exhaust camshaft 142) may control multiple exhaust valvesfor the cylinder 118 and/or may control exhaust valves (including theexhaust valve 130) for multiple banks of cylinders (including thecylinder 118). The cylinder actuator module 120 may deactivate thecylinder 118 by disabling opening of the intake valve 122 and/or theexhaust valve 130. In various other implementations, the intake valve122 and/or the exhaust valve 130 may be controlled by devices other thancamshafts, such as camless valve actuators.

The time when the intake valve 122 is opened may be varied with respectto piston TDC by an intake cam phaser 148. The time when the exhaustvalve 130 is opened may be varied with respect to piston TDC by anexhaust cam phaser 150. A phaser actuator module 158 may control theintake cam phaser 148 and the exhaust cam phaser 150 based on signalsfrom the ECM 114. When implemented, variable valve lift (not shown) mayalso be controlled by the phaser actuator module 158.

The engine system 100 may include a boost device that providespressurized air to the intake manifold 110. For example, FIG. 1 shows aturbocharger including a hot turbine 160-1 that is powered by hotexhaust gases flowing through the exhaust system 134. The turbochargeralso includes a cold air compressor 160-2 that is driven by the turbine160-1. The compressor 160-2 compresses air leading into the throttlevalve 112. In various implementations, a supercharger (not shown),driven by the crankshaft, may compress air from the throttle valve 112and deliver the compressed air to the intake manifold 110.

A wastegate 162 may allow exhaust to bypass the turbine 160-1, therebyreducing the boost (the amount of intake air compression) provided bythe turbocharger. The ECM 114 may control the turbocharger via a boostactuator module 164. The boost actuator module 164 may modulate theboost of the turbocharger by controlling opening of the wastegate 162.In various implementations, multiple turbochargers may be controlled bythe boost actuator module 164. The turbocharger may have variablegeometry, which may be controlled by the boost actuator module 164.

An intercooler (not shown) may dissipate some of the heat contained inthe compressed air charge, which is generated as the air is compressed.The compressed air charge may also have absorbed heat from components ofthe exhaust system 134. Although shown separated for purposes ofillustration, the turbine 160-1 and the compressor 160-2 may be attachedto each other, placing intake air in close proximity to hot exhaust.

The engine system 100 may include an exhaust gas recirculation (EGR)valve 170, which selectively redirects exhaust gas back to the intakemanifold 110. The EGR valve 170 may be located upstream of theturbocharger's turbine 160-1. The EGR valve 170 may be controlled by anEGR actuator module 172.

The engine system 100 may measure the rotational speed of the crankshaftin revolutions per minute (RPM) using an RPM sensor 180. The speed ofthe crankshaft may be referred to as an engine speed. The temperature ofthe engine coolant may be measured using an engine coolant temperature(ECT) sensor 182. The ECT sensor 182 may be located within the engine102 or at other locations where the coolant is circulated, such as aradiator (not shown).

The pressure within the intake manifold 110 may be measured using amanifold absolute pressure (MAP) sensor 184. In various implementations,engine vacuum, which is the difference between ambient air pressure andthe pressure within the intake manifold 110, may be measured. The massflow rate of air flowing into the intake manifold 110 may be measuredusing a mass air flow (MAF) sensor 186. In various implementations, theMAF sensor 186 may be located in a housing that also includes thethrottle valve 112.

The throttle actuator module 116 may monitor the position of thethrottle valve 112 using one or more throttle position sensors (TPS)190. The ambient temperature of air being drawn into the engine 102 maybe measured using an intake air temperature (IAT) sensor 192. The enginesystem 100 may also include one or more other sensors. The ECM 114 mayuse signals from the sensors to make control decisions for the enginesystem 100.

The ECM 114 may communicate with a transmission control module 194 tocoordinate shifting gears in a transmission (not shown). For example,the ECM 114 may reduce engine torque during a gear shift. The ECM 114may communicate with a hybrid control module 196 to coordinate operationof the engine 102 and an electric motor 198. While the example of oneelectric motor is provided, the vehicle may include more than oneelectric motor.

The electric motor 198 may also function as a generator, and may be usedto produce electrical energy for use by vehicle electrical systemsand/or for storage in a battery. In various implementations, variousfunctions of the ECM 114, the transmission control module 194, and thehybrid control module 196 may be integrated into one or more modules.

Each system that varies an engine parameter may be referred to as anactuator. Each system receives a target actuator value. For example, thethrottle actuator module 116 may be referred to as an actuator, and atarget throttle opening (e.g., area) may be referred to as the targetactuator value. In the example of FIG. 1, the throttle actuator module116 achieves the target throttle opening by adjusting an angle of theblade of the throttle valve 112.

Similarly, the spark actuator module 126 may be referred to as anactuator, while the corresponding target actuator value may be a targetspark timing, for example, relative to piston TDC. Other actuators mayinclude the cylinder actuator module 120, the fuel actuator module 124,the phaser actuator module 158, the boost actuator module 164, and theEGR actuator module 172. For these actuators, the target actuator valuesmay include target number of activated cylinders, target fuelingparameters, target intake and exhaust cam phaser angles, targetwastegate duty cycle, and target EGR valve opening area, respectively.The ECM 114 may generate the target actuator values to cause the engine102 to generate a target engine output torque.

Referring now to FIG. 2, a functional block diagram of an example enginecontrol system is presented. An example implementation of the ECM 114includes a driver torque module 202 and a torque arbitration module 204.The ECM 114 may include a hybrid optimization module 208. The ECM 114may include a torque requesting module 224, an air control module 228, aspark control module 232, a cylinder control module 236, and a fuelcontrol module 240. The ECM 114 also includes a torque estimation module244, a boost control module 248, a phaser control module 252, and an EGRcontrol module 253.

The driver torque module 202 may determine a driver torque request 254based on a driver input 255 from the driver input module 104. The driverinput 255 may be based on or include, for example, a position of anaccelerator pedal and a position of a brake pedal. The driver input 255may also be based on or include a cruise control input, which may begenerated by an adaptive cruise control system based on varying vehiclespeed to maintain a predetermined following distance. The driver torquemodule 202 may include one or more mappings of accelerator pedalposition to target torque and may determine the driver torque request254 based on a selected one of the mappings.

The torque arbitration module 204 may arbitrate between the drivertorque request 254 and other torque requests 258. The axle torquearbitration module 204 outputs one or more torque requests 257 based onthe results of the arbitration between the received torque requests 254and 258.

The torque arbitration module 204 may output the one or more torquerequests 257 to the hybrid optimization module 208. The hybridoptimization module 208 may determine how much torque should be producedby the engine 102 and how much torque should be produced by the electricmotor 198. The hybrid optimization module 208 outputs one or moremodified engine torque requests 260 and a motor torque request 261. Thehybrid control module 196 controls torque output of the electricmotor(s) based on (e.g., to achieve) the motor torque request 261. Theengine 102 is controlled based on (e.g., to achieve) the one or moremodified engine torque requests 260. In various implementations, thehybrid optimization module 208 may be implemented in the hybrid controlmodule 196. In various implementations, the one or more modified enginetorque requests 260 may be adjusted based on a torque reserve and/or atorque load. In various implementations, one or more conversions fromaxle torque (torque at the wheels) to propulsion torque (torque at thecrankshaft) may be performed.

The torque requesting module 224 receives the one or more modifiedengine torque requests 260. The torque requesting module 224 determineshow the one or more modified engine torque requests 260 will be achievedby the engine 102. The torque requesting module 224 may be engine typespecific. For example, the torque requesting module 224 may beimplemented differently or use different control schemes forspark-ignition engines versus compression-ignition engines.

In various implementations, the torque requesting module 224 maygenerate an air torque request 265 based on the one or more modifiedengine torque requests 260. Target actuator values for airflowcontrolling actuators may be determined based on the air torque request265. For example only, the air control module 228 may determine a targetmanifold absolute pressure (MAP) 266, a target throttle opening (e.g.,area) 267, a target air per cylinder (APC) 268, and a target APC (APC)291 based on the air torque request 265. The air control module 228 maydetermine the targets 266-268 and 291 using one or more equations and/orlookup tables that relate air torque requests to values of the targets266-268 and 291.

The boost control module 248 may determine a target duty cycle 269 forthe wastegate 162 based on the target MAP 266. While the target dutycycle 269 will be discussed, the boost control module 248 may determineanother suitable value for controlling the wastegate 162. The phasercontrol module 252 may determine target intake and exhaust cam phaserangles 270 and 271 based on the target APC 268. The EGR control module253 determines a target EGR opening 292 based on the target APC 291. Thetargets 269-271 and 292 may be determined by the respective modulesusing one or more equations and/or lookup tables that relate therespective inputs to the respective targets 269-271 and 292.

The torque requesting module 224 may also generate a spark torquerequest 272, a cylinder shut-off torque request 273, and a fuel torquerequest 274. The spark control module 232 may determine how much toretard the spark timing (which reduces engine output torque) from amaximum brake torque (MBT) spark timing based on the spark torquerequest 272. For example only, a torque model, such as the torque modeldiscussed below, may be inverted to solve for a target spark timing 299.The MBT spark timing may refer to an estimated spark timing used togenerate a maximum brake torque for predetermined operating conditions.The MBT spark timing is discussed further below.

The cylinder shut-off torque request 273 may be used by the cylindercontrol module 236 to determine a target number of cylinders todeactivate 276. The cylinder control module 236 may also instruct thefuel control module 240 to stop providing fuel for deactivated cylindersand may instruct the spark control module 232 to stop providing sparkfor deactivated cylinders. The spark control module 232 may stopproviding spark to a cylinder once an fuel/air mixture that is alreadypresent in the cylinder has been combusted.

The fuel control module 240 may control fuel injection into a nextcylinder in the predetermined firing order based on the fuel torquerequest 274. More specifically, the fuel control module 240 may generatetarget fueling parameters 277 based on the fuel torque request 274. Thetarget fueling parameters 277 may include, for example, a targetequivalence ratio (EQR), a target mass of fuel, a target start ofinjection (SOI) timing, a target end of injection (EOI) timing, and atarget number of fuel injections.

The air control module 228 generates the target MAP 266, the targetthrottle opening 267, the target APC 268, and the target APC 291 basedon the estimated torque 278. The estimated torque 278 may be anestimated value of the present engine torque output (i.e., torque outputof the engine 102) and is determined as described below.

The air control module 228 may output the target throttle opening 267 tothe throttle actuator module 116. The throttle actuator module 116regulates the throttle valve 112 to produce the target throttle opening267. The air control module 228 outputs the target MAP 266 to the boostcontrol module 248. The boost control module 248 controls the wastegate162 based on (e.g., to achieve) the target MAP 266. The air controlmodule 228 outputs the target APC 268 to the phaser control module 252.Based on the target APC 268, the phaser control module 252 may controlpositions of the intake and/or exhaust cam phasers 148 and 150.

As discussed further below, the torque estimation module 244 uses atorque model to determine the estimated torque 278 based on a presentengine speed (RPM) 280, a present EQR 281, a present air per cylinder(APC) 282, a present spark timing 283, a present intake cam phaser angle284, and a present exhaust cam phaser angle 285. The torque estimationmodule 244 may additionally determine the estimated torque 278 based ona present SOI timing 308 of fueling and a present EOI timing 312 offueling. In various implementations, the torque estimation module 244may additionally determine the estimated torque 278 based on a presentMBT spark timing 316.

FIG. 3 is a functional block diagram of an example implementation of thetorque estimation module 244. A normalization module 304 receives theAPC 282, the engine speed 280, the intake cam phaser angle 284, theexhaust cam phaser angle 285, the spark timing 283, and the EQR 281. Thenormalization module 304 may also receive a present start of injection(SOI) timing 308 of fueling, and a present end of injection (EOI) timing312 of fueling. The normalization module 304 may also receive a presentMBT spark timing 316.

An MBT module 320 (FIG. 2) may determine the MBT spark timing 316. TheMBT spark timing 316 may be the spark timing used to generate the MBTfor the predetermined operating conditions. Using combustionmeasurements and sweeping the spark timing for a fixed engine speed,APC, intake cam phaser angle, and exhaust cam phaser angle, the sparkclosest to MBT is that which yields a CA50 (crankshaft angle after TDCat which 50 percent of injected fuel is consumed/combusted) closest to8.5 degrees. The MBT module 320 may determine the MBT spark timing 316using the equation:MBT=C_Spark+(C_CA50−8.5)+offset,where MBT is the MBT spark timing 316, C_Spark and C_CA50 are the sparktiming and CA50 values in the spark timing sweep where CA50 is closestto 8.5 degrees. Offset is a predetermined value and may be calibratedbased on compensating for operating conditions where the MBT sparktiming does not coincide with a CA50 value of 8.5 degrees. As analternative, the MBT module 320 may determine the MBT spark timing 316based on APC, an inverse APC, the engine speed, the intake and exhaustcam phaser angles, the equivalence ratio, and an opening of the EGRvalve. The determination may be made using one or more equations (e.g.,a neural network or another suitable type of model) and/or one or morelookup tables The MBT spark timing 316 may have an inverse relationshipwith the APC 282.

Collectively, the APC 282, the engine speed 280, the intake cam phaserangle 284, the exhaust cam phaser angle 285, the spark timing 283, andthe EQR 281, the SOI timing 308 (if included), the EOI timing 312 (ifincluded), and the MBT spark timing 316 will be referred to as inputparameters 322. The normalization module 304 normalizes each of theinput parameters 322 to within a predetermined range. The predeterminedrange may be, for example, 0 to 1, inclusive, −1 to +1, inclusive, oranother suitable range. The normalization module 304 normalizes a givenone of the input parameters 322 using interpolation betweenpredetermined minimum and maximum values of that input parameter. Forexample, when the input parameter is equal to the predetermined minimumvalue, the normalization module 304 may set the normalized parameter tothe lower limit value of the predetermined range (e.g., 0 or −1). Whenthe input parameter is equal to the predetermined maximum value, thenormalization module 304 may set the normalized parameter to the upperlimit value of the predetermined range (e.g., 1). When the inputparameter is between the predetermined minimum and maximum values, thenormalization module 304 may set the normalized parameter between theupper and lower limit values of the predetermined range viainterpolation, such as linear interpolation. The normalization module304 does this for each of the input parameters 322 to produce normalizedparameters 324. The normalized parameters 324 include a normalized APC,a normalized engine speed, a normalized intake cam phaser angle, anormalized exhaust cam phaser angle, a normalized spark timing, anormalized EQR, a normalized SOI timing (if included), a normalized EOItiming (if included), and a normalized MBT spark timing.

A processing module 326 performs one or more signal processing functionson one or more of the normalized parameters 324 to produce one or moreprocessed parameters 328, respectively. For example, the processingmodule 326 may apply a sigmoid function to one or more of the normalizedparameters 324 to produce one or more sigmoidal parameters,respectively. For example, the processing module 326 may apply a sigmoidfunction to the normalized spark timing to produce a sigmoidal sparktiming. The sigmoid function may be, for example, a logistic function oranother suitable type of sigmoid function. The processing module 326 mayapply an exponential function to one or more of the normalizedparameters 324 to produce one or more exponential parameters,respectively. For example, the processing module 326 may apply theexponential function to the normalized intake cam phaser angle, thenormalized exhaust cam phaser angle, the normalized engine speed, thenormalized MBT spark timing, the normalized SOI timing, and thenormalized EOI timing to produce an exponential intake cam phaser angle,an exponential exhaust cam phaser angle, an exponential engine speed, anexponential MBT spark timing, an exponential normalized SOI timing, andan exponential normalized EOI timing, respectively. The processingmodule 326 may apply a negative exponential function to one or more ofthe normalized parameters 324 to produce one or more negativeexponential parameters, respectively. For example, the processing module326 may apply the negative exponential function to the normalized enginespeed, the normalized MBT spark timing, the normalized SOI timing, andthe normalized EOI timing to produce a negative exponential enginespeed, a negative exponential MBT spark timing, a negative exponentialSOI timing, and a negative exponential EOI, respectively. The processingmodule 326 may apply a sinusoidal function to one or more of thenormalized parameters 324 to produce one or more sinusoidal parameters,respectively. For example, the processing module 326 may apply thesinusoidal function to the normalized intake cam phaser angle, thenormalized exhaust cam phaser angle, the normalized engine speed, thenormalized MBT spark timing, the normalized SOI timing, and thenormalized EOI timing to produce a sinusoidal intake cam phaser angle, asinusoidal exhaust cam phaser angle, a sinusoidal engine speed, asinusoidal MBT spark timing, a sinusoidal normalized SOI timing, and asinusoidal normalized EOI timing, respectively.

The exponential function may be described as y=e^(x), where y is theexponential parameter, e is the exponent function, and x is thenormalized parameter. The negative exponential function may be describedas y=e^(−x) where y is the exponential parameter, e is the exponentfunction, and x is the normalized parameter. The sigmoid function may bedescribed as y=1/(1+e^(−mx)), where y is the exponential parameter, e isthe exponent function, m is a predetermined multiplier value, and x isthe normalized parameter. m is may be a calibrated value.

An estimation module 332 determines the estimated torque 278 based onone or more of the input parameters 322, one or more of the normalizedparameters 324, and/or one or more of the processed parameters 328 usinga mathematical model 336. For example, the estimation module 332 maydetermine the estimated torque 278 based on the following inputs (x),x=[the normalized intake cam phaser angle, the exponential intake camphaser angle, the normalized exhaust cam phaser angle, the exponentialexhaust cam phaser angle, the sigmoidal spark timing, the normalizedAPC, the normalized engine speed, the exponential engine speed, thenegative exponential engine speed, the normalized EQR, the normalizedMBT spark timing, the exponential MBT spark timing, the negativeexponential spark timing]. The model may be, for example, a second orderor a third order polynomial for each of the inputs (x). An example of athird order polynomial is:f(x ₁ ,x ₂ ,x ₃)=ax ₁ ³ +bx ₂ ³ +cz ³ +dx ₁ ² +ex ₁ ² x ² +fx ₁ ² z+gx ₂² +hx ₂ ² x ₁ +ix ₂ ² x ³ +jx ₃ ² +kx ₃ ² x ₁ +lz ² x ₂ +mx ₁ x ₂ +nx ₁x ₃ +ox ₂ x ₃ +px ₁ +qx ₂ +rx ₃ +s,where a-s are predetermined values, and x1-x3 are ones of the inputparameters. Use of the above third order polynomial equation may resultin the model 336 having 559 terms. One or more methods may be used toeliminate any underperforming terms in the polynomial equation, such asvia Lasso regression or in another suitable manner.

One or more actuators can be controlled based on the estimated torque278. For example, the air control module 228 may control opening of thewastegate 162 based on the estimated torque 278. The air control module228 may control opening of the throttle valve 112 based on the estimatedtorque 278. The air control module 228 may control opening of the EGRvalve 170 based on the estimated torque 278. The air control module 228may control actuation of the intake and/or exhaust cam phasers 148 and150 based on the estimated torque 278. The spark control module 232 maycontrol spark timing based on the estimated torque 278. The fuel controlmodule 240 may control fuel injection based on the estimated torque 278.The cylinder control module 236 may control activation/deactivation ofcylinders based on the estimated torque 278. The inversion above helpsachieve the target air and spark values from the torque request, and theforward estimation provides feedback to assess whether the torquerequest is being achieved.

FIG. 4 is a flowchart depicting an example method of estimating torqueoutput of the engine 102 and controlling engine actuators. Controlbegins with 404 where the normalization module 304 receives the inputparameters 322. At 408, the normalization module 304 normalizes theinput parameters 322 to produce the normalized parameters 324,respectively.

At 412, the processing module 326 receives the normalized parameters 324and performs signal processing on one or more of the normalizedparameters 324 to produce the one or more processed parameters 328,respectively. At 416, the estimation module 332 determines the estimatedtorque 278 based on the normalized parameters and the one or moreprocessed parameters 328 using the model 336, as discussed above. Forexample, the estimation module 332 may determine the estimated torque278 using the model 336 based on the normalized intake cam phaser angle,the exponential intake cam phaser angle, the normalized exhaust camphaser angle, the exponential exhaust cam phaser angle, the sigmoidalspark timing, the normalized APC, the normalized engine speed, theexponential engine speed, the negative exponential engine speed, thenormalized EQR, the normalized MBT spark timing, the exponential MBTspark timing, and the negative exponential spark timing.

At 420, one or more actuators are adjusted based on the estimated torque278. For example, the air control module 228 may adjust opening of thewastegate 162 based on the estimated torque 278. The air control module228 may adjust opening of the throttle valve 112 based on the estimatedtorque 278. The air control module 228 may adjust opening of the EGRvalve 170 based on the estimated torque 278. The air control module 228may adjust positioning of the intake and/or exhaust cam phasers 148 and150 based on the estimated torque 278. The spark control module 232 mayadjust spark timing based on the estimated torque 278. The fuel controlmodule 240 may adjust fuel injection based on the estimated torque 278.The cylinder control module 236 may adjust activation/deactivation ofcylinders based on the estimated torque 278. While control is shown asending after 420, control may return to 404, and 404-420 may be startedevery predetermined period.

Referring back to FIG. 3, a parameter estimation module 350 may estimateone of the input parameters 322. More specifically, a parameter module352 may estimate one parameter 351 of the input parameters 322 based ona torque 354 and other ones of the input parameters 322 by inverting themodel 336. An inversion module 358 may invert the model 336 for thedetermination of the one of the input parameters 322. The torque 354 maybe, for example, one of the torque requests discussed above, a desiredtorque, a target torque, etc.

When a torque is requested and all inputs except for one are specified,the model 336 can be used to solve for the one unspecified input. Thefirst, second, third order and constant terms in the model 336 can begrouped to form the equation:ax ³ +bx ² +cx+d=0.

Solving a third order equation can result in 1 or 3 real roots. Firstthe general form of the cubic may be modified to remove the leadingcoefficient (a). x³+c₁x²+c₂x+c₃=0, where c₁=b/a, c₂=c/a and c₃=d/a. Thenthe discriminant (M) can be calculated. as follows:Q=(c ₁ ²−3c ₂)/9,R=(2c ₁ ³−9c ₁ c ₂+27c ₃)/54,M=R ² −Q ³If M<0, there are three roots, and if M>0 there is only one root. If 3real inputs are present, the inversion module 358 selects which of the 3roots to use as an engine control target.

For example, the inversion module 358 may select a root by creating asupplemental forward regressor for the variable that the model 336 isbeing inverted to find (the one unspecified input). For example, aforward APC regressor can be used to estimate a target APC given a setof intake and exhaust cam phaser angles, an engine speed, a sparktiming, and a torque request. Additionally, the inversion module 358 maycreate a regressor using the characteristics of the cubic equation beingsolved, including the coefficients (a, b, c, d), the inflection andturning points. In the 3-root case, the closest root to the output ofthe forward regressor may be chosen as a control target.

The inversion module 358 may rule out infeasible roots based onpredetermined control limits. For example, when solving for sparktiming, any root found must be less than the MBT spark timing. The MBTspark can be determined as described above or by using the first andsecond derivative of the univariate third order polynomial with respectto spark timing. Solving the first derivative where the rate of changeis equal to zero may yield spark timing values that would cause theminimum and maximum torque (turning points).3ax ²+2bx+c=0

After solving the quadratic equation, the second derivative can be usedto distinguish between the roots.d ² f/dx=6ax+2b

Solving for x with the second derivative equal to zero yields the xcoordinate of the inflection point (x=−b/3a). If the second derivativefor a root is greater than zero, that is the spark advance at which mintorque is generated. If the second derivative for a root is less thanzero, that is the spark at which the MBT is generated.

To avoid the complexity associated with the 3-root example, theinversion module 358 may enforce a regression constraint that will onlyallow the cubic to have a single root solution. The inversion module 358may constrain coefficients such that M>0, so that only a single rootsolution is possible. Alternatively, the inversion module 358 mayeliminate the third order term for the input that the model 336 is beinginverted to find, so that a quadratic formula can be used to find up to2 real roots. The inversion module 358 may determine which of the 2roots to select.

The foregoing description is merely illustrative in nature and is in noway intended to limit the disclosure, its application, or uses. Thebroad teachings of the disclosure can be implemented in a variety offorms. Therefore, while this disclosure includes particular examples,the true scope of the disclosure should not be so limited since othermodifications will become apparent upon a study of the drawings, thespecification, and the following claims. It should be understood thatone or more steps within a method may be executed in different order (orconcurrently) without altering the principles of the present disclosure.Further, although each of the embodiments is described above as havingcertain features, any one or more of those features described withrespect to any embodiment of the disclosure can be implemented in and/orcombined with features of any of the other embodiments, even if thatcombination is not explicitly described. In other words, the describedembodiments are not mutually exclusive, and permutations of one or moreembodiments with one another remain within the scope of this disclosure.

Spatial and functional relationships between elements (for example,between modules, circuit elements, semiconductor layers, etc.) aredescribed using various terms, including “connected,” “engaged,”“coupled,” “adjacent,” “next to,” “on top of,” “above,” “below,” and“disposed.” Unless explicitly described as being “direct,” when arelationship between first and second elements is described in the abovedisclosure, that relationship can be a direct relationship where noother intervening elements are present between the first and secondelements, but can also be an indirect relationship where one or moreintervening elements are present (either spatially or functionally)between the first and second elements. As used herein, the phrase atleast one of A, B, and C should be construed to mean a logical (A OR BOR C), using a non-exclusive logical OR, and should not be construed tomean “at least one of A, at least one of B, and at least one of C.”

In the figures, the direction of an arrow, as indicated by thearrowhead, generally demonstrates the flow of information (such as dataor instructions) that is of interest to the illustration. For example,when element A and element B exchange a variety of information butinformation transmitted from element A to element B is relevant to theillustration, the arrow may point from element A to element B. Thisunidirectional arrow does not imply that no other information istransmitted from element B to element A. Further, for information sentfrom element A to element B, element B may send requests for, or receiptacknowledgements of, the information to element A.

In this application, including the definitions below, the term “module”or the term “controller” may be replaced with the term “circuit.” Theterm “module” may refer to, be part of, or include: an ApplicationSpecific Integrated Circuit (ASIC); a digital, analog, or mixedanalog/digital discrete circuit; a digital, analog, or mixedanalog/digital integrated circuit; a combinational logic circuit; afield programmable gate array (FPGA); a processor circuit (shared,dedicated, or group) that executes code; a memory circuit (shared,dedicated, or group) that stores code executed by the processor circuit;other suitable hardware components that provide the describedfunctionality; or a combination of some or all of the above, such as ina system-on-chip.

The module may include one or more interface circuits. In some examples,the interface circuits may include wired or wireless interfaces that areconnected to a local area network (LAN), the Internet, a wide areanetwork (WAN), or combinations thereof. The functionality of any givenmodule of the present disclosure may be distributed among multiplemodules that are connected via interface circuits. For example, multiplemodules may allow load balancing. In a further example, a server (alsoknown as remote, or cloud) module may accomplish some functionality onbehalf of a client module.

The term code, as used above, may include software, firmware, and/ormicrocode, and may refer to programs, routines, functions, classes, datastructures, and/or objects. The term shared processor circuitencompasses a single processor circuit that executes some or all codefrom multiple modules. The term group processor circuit encompasses aprocessor circuit that, in combination with additional processorcircuits, executes some or all code from one or more modules. Referencesto multiple processor circuits encompass multiple processor circuits ondiscrete dies, multiple processor circuits on a single die, multiplecores of a single processor circuit, multiple threads of a singleprocessor circuit, or a combination of the above. The term shared memorycircuit encompasses a single memory circuit that stores some or all codefrom multiple modules. The term group memory circuit encompasses amemory circuit that, in combination with additional memories, storessome or all code from one or more modules.

The term memory circuit is a subset of the term computer-readablemedium. The term computer-readable medium, as used herein, does notencompass transitory electrical or electromagnetic signals propagatingthrough a medium (such as on a carrier wave); the term computer-readablemedium may therefore be considered tangible and non-transitory.Non-limiting examples of a non-transitory, tangible computer-readablemedium are nonvolatile memory circuits (such as a flash memory circuit,an erasable programmable read-only memory circuit, or a mask read-onlymemory circuit), volatile memory circuits (such as a static randomaccess memory circuit or a dynamic random access memory circuit),magnetic storage media (such as an analog or digital magnetic tape or ahard disk drive), and optical storage media (such as a CD, a DVD, or aBlu-ray Disc).

The apparatuses and methods described in this application may bepartially or fully implemented by a special purpose computer created byconfiguring a general purpose computer to execute one or more particularfunctions embodied in computer programs. The functional blocks,flowchart components, and other elements described above serve assoftware specifications, which can be translated into the computerprograms by the routine work of a skilled technician or programmer.

The computer programs include processor-executable instructions that arestored on at least one non-transitory, tangible computer-readablemedium. The computer programs may also include or rely on stored data.The computer programs may encompass a basic input/output system (BIOS)that interacts with hardware of the special purpose computer, devicedrivers that interact with particular devices of the special purposecomputer, one or more operating systems, user applications, backgroundservices, background applications, etc.

The computer programs may include: (i) descriptive text to be parsed,such as HTML (hypertext markup language), XML (extensible markuplanguage), or JSON (JavaScript Object Notation) (ii) assembly code,(iii) object code generated from source code by a compiler, (iv) sourcecode for execution by an interpreter, (v) source code for compilationand execution by a just-in-time compiler, etc. As examples only, sourcecode may be written using syntax from languages including C, C++, C#,Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl,Pascal, Curl, OCaml, Javascript®, HTML5 (Hypertext Markup Language 5threvision), Ada, ASP (Active Server Pages), PHP (PHP: HypertextPreprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, VisualBasic®, Lua, MATLAB, SIMULINK, and Python®.

What is claimed is:
 1. An engine control system, comprising: anormalization module configured to normalize, to within a predeterminedrange of values, a spark timing of an engine and at least one otherparameter of the engine, thereby producing a normalized spark timing andat least one normalized other parameter, respectively; a processingmodule configured to generate a sigmoidal spark timing by applying, tothe normalized spark timing, one of (a) a sigmoidal function and asinusoidal function; and an estimation module configured to estimate atorque output of the engine based on the normalized spark timing and theat least one normalized other parameter using a mathematical model. 2.The engine control system of claim 1 further comprising an actuatormodule configured to adjust an engine actuator based on the estimatedtorque output of the engine.
 3. The engine control system of claim 1wherein the at least one other parameter of the engine includes anengine speed.
 4. The engine control system of claim 1 wherein the atleast one other parameter of the engine includes a mass of air percylinder (APC) of the engine.
 5. The engine control system of claim 1wherein the at least one other parameter of the engine includes anintake cam phaser angle.
 6. The engine control system of claim 1 whereinthe at least one other parameter of the engine includes an exhaust camphaser angle.
 7. The engine control system of claim 1 wherein the atleast one other parameter of the engine includes an equivalence ratio(EQR) of the engine.
 8. The engine control system of claim 1 wherein theat least one other parameter of the engine includes a maximum brakingtorque (MBT) spark timing of the engine.
 9. The engine control system ofclaim 1 wherein the at least one other parameter of the engine includes:an engine speed; a mass of air per cylinder (APO) of the engine; anintake cam phaser angle; an exhaust cam phaser angle; an equivalenceratio (EQR) of the engine; and a maximum braking torque (MBT) sparktiming of the engine.
 10. The engine control system of claim 1 whereinthe sigmoid function includes a logistic function.
 11. The enginecontrol system of claim 1 wherein the at least one other parameter ofthe engine includes a timing of a start of fuel injection of the engine.12. The engine control system of claim 1 wherein the at least one otherparameter of the engine includes a timing of an end of fuel injection ofthe engine.
 13. The engine control system of claim 1 wherein theprocessing module is further configured to generate an exponentialengine speed by applying an exponential function to an engine speed, andwherein the estimation module configured to estimate the torque outputof the engine further based on the exponential engine speed using themathematical model.
 14. The engine control system of claim 1 wherein theprocessing module is further configured to generate an exponential ofnegative engine speed by applying an exponential function to a negativeengine speed, and wherein the estimation module configured to estimatethe torque output of the engine further based on the exponential ofnegative engine speed using the mathematical model.
 15. The enginecontrol system of claim 1 wherein the processing module is furtherconfigured to generate an exponential maximum braking torque (MBT) sparktiming by applying an exponential function to an MBT spark timing of theengine, and wherein the estimation module configured to estimate thetorque output of the engine further based on the exponential MBT sparktiming using the mathematical model.
 16. The engine control system ofclaim 1 wherein the processing module is further configured to generatean exponential of negative maximum braking torque (MBT) spark timing byapplying an exponential function to a negative MBT spark timing of theengine, and wherein the estimation module configured to estimate thetorque output of the engine further based on the exponential of negativeMBT spark timing using the mathematical model.
 17. An engine controlsystem, comprising: a normalization module configured to normalize, towithin a predetermined range of values, a maximum braking torque (MBT)spark timing of an engine and at least one other parameter of theengine, thereby producing a normalized MBT spark timing and at least onenormalized other parameter, respectively; and an estimation moduleconfigured to estimate a torque output of the engine based on thenormalized MBT spark timing and the at least one normalized otherparameter using a mathematical model.
 18. The engine control system ofclaim 17 further comprising a processing module configured to generatean exponential MBT spark timing by applying an exponential function tothe MBT spark timing of the engine, and wherein the estimation moduleconfigured to estimate the torque output of the engine further based onthe exponential MBT spark timing using the mathematical model.
 19. Theengine control system of claim 17 further comprising a processing moduleconfigured to: generate an exponential MBT spark timing by applying anexponential function to the MBT spark timing of the engine; and generatean exponential of negative MBT spark timing by applying an exponentialfunction to the negative MBT spark timing of the engine, wherein theestimation module configured to estimate the torque output of the enginefurther based on the exponential MBT spark timing and the exponential ofnegative MBT spark timing using the mathematical model.
 20. The enginecontrol system of claim 17 further comprising an MBT module configuredto generate the MBT spark timing based on an air per cylinder, aninverse APC, an engine speed, an intake cam phaser angle, an exhaust camphaser angle, an equivalence ratio, and an opening of an EGR valve.